LAGRANGIAN THEORY OF GRAVITATIONAL-INSTABILITY OF FRIEDMAN-LEMAITRE COSMOLOGIES - A GENERIC 3RD-ORDER MODEL FOR NONLINEAR CLUSTERING

The Lagrangian perturbation theory of Friedman-Lemaitre cosmologies, w hich was investigated and solved up to the second order in earlier pap ers, is evaluated up to the third order. Based on this, a model for no n-linear clustering applicable to the modelling of large-scale structu re in the Universe for generic initial conditions is formulated. A tru ncated model is proposed which represents the 'main body' of the pertu rbation sequence in the early non-linear regime by neglecting all grav itational sources that describe interaction of the perturbations. I al so, however, give the irrotational solutions generated by the interact ion terms to the third order, which induce vorticity in Lagrangian spa ce. The consequences and applicability of the solutions are put into p erspective. In particular, the model presented enables the study of pr e-virialization effects in gravitational clustering and the onset of n on-dissipative gravitational turbulence within the cluster environment .